Properties of Real Numbers

Relationships that are always true for real numbers are called _____________, which are rules used to rewrite and compare expressions. properties

Order stays the same only ( ) move PROPERTY DEFINITION EXAMPLE Commutative Property Addition Multiplication Associative Distributive Property 1 + 2 = 2 + 1 a + b = b + a Changing Order does not change the outcome 1 ● 2 = 2 ● 1 a b = b a (8 + 6) + 7 = 8 + (6 + 7) (a + b) + c = a + (b + c) Regrouping Order stays the same only ( ) move 4● (5 ●9) = (4 ●5) ● 9 (ab) ● c = a ● (bc ) (Change who you associate [hang out] with) a(b + c) = ab + ac a(b - c) = ab - ac 10 (1 + 7) = 10 ● 1 + 10 ●7 15(x - 4) = 15 ● x – 15 ●4

-17 + 0 = -17 1● 99y = 99y a + (-a) = 0 14 + (-14) = 0 Property Definition Example Identity Properties Addition Multiplication Inverse Properties Adding “0” = no change -17 + 0 = -17 Multiply by 1= no change 1● 99y = 99y a + (-a) = 0 14 + (-14) = 0

Multiply by 0, you get 0 (7003)(0) = 0 -1(a) = -a -1(2) = -2 Property Definition Example Zero Property of Multiplication Multiplication Property of –1 Multiply by 0, you get 0 (7003)(0) = 0 -1(a) = -a -1(2) = -2 -1(-5) = 5 Multiply by -1, you change the sign

Identifying Properties (What property is shown in each example?) Zero Property of Multiplication Associative Prop. of Addition Identity of Addition (Additive Identity) Identity of Multiplication (Multiplicative Identity) Commutative Prop. (Addition) The “z” and the √ y have been switched.

Using Properties for Mental Calculations F. A movie ticket costs $7.75. A drink costs $2.40. Popcorn costs $1.25. What is the total cost for a ticket, a drink, and popcorn? Use mental math.   G. A can hold 3 tennis balls. A box holds 4 cans. A case holds 6 boxes. How many tennis balls are in 10 cases? Use mental math. $7.75 + $2.40 + $1.25 = (7.75 +1.25 + 2.40) = 9.00 + 2.40 = 11.40 3●4 ●6 ●10 = 720

Writing Equivalent Expressions (7b + 4) + 8 7b + ( 4 + 8) 7b + 12 1 6x (2.1 ● 4.5)x 9.45x 6 + (3 + 4h) (6 + 3) + 4h 9+ 4h